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Find the smallest angle \(x\) such that \(x>90\) and \(6\tan^2(5x-3) = 2\)

 Oct 29, 2019
 #1
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6 tan ^2  ( 5x - 3)  = 2

 

tan^2 ( 5x - 3)  = 1/3      take both roots

 

tan (5x - 3)  =  ±√[1/3]

 

So  we have the following possibilities

 

arctan ( 1 / √3) =  5x - 3         or         arctan (-1/√3) = 5x - 3

 

150 = 5x - 3                                         330 = = 5x - 3

150 +3  = 5x                                        330 + 3  = 5x

153  = 5x                                              333  = 5x                                    

x = 153/5                                              333/5 = x

x = 30.6                                                  x = 66.6

 

 

510 = 5x - 3

510 + 3  = 5x

513 = 5x

513/5  = x

x = 102. 6°

 

 

cool cool cool

 Oct 29, 2019

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